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We are studying reactions of Ti, V, Zr, and Hf with ceramics as part of a program to understand fundamental reaction and bonding mechanisms in active metal brazing of ceramics. In this paper we present results of experiments with model systems comprising Ag alloys that contain different amounts of Hf or Zr that were reacted with sapphire or 99.6% alumina for different times and temperatures in a controlled atmosphere furnace. In these alloys the Ag functions as an inert solvent, which allowed us systematically to determine the effects of changes in concentration of the active element. We observed qualitative wetting and spreading tendencies of the alloys during heating and examined cross sections after cooling using electron analytical techniques. For all reaction times studied, the Hf/Ag alloys formed a discontinuous reaction layer, which was consistent with earlier high-resolution electron microscopy that showed sub-micrometer HfO2 particles embedded in the surfaces of the Al2O3 grains. By contrast, initial reaction of the Zr/Ag alloys with Al2O3 produced a continuous interface layer. With longer reaction times, the ZrO2 reaction product became much thicker and exhibited three distinct zones at the interface. The results suggest that the rate limiting step in the Zr/Ag reaction is the chemical reaction at the interface, whereas with Hf/Ag reaction diffusion of products away from the interface is rate limiting.